I enter this topic late, but I'd say there are several reasons Gotti was liked and popular.
He was a career gangster who truly lived the life, which garners respect. He was a flash dresser as he got older, not a dirty street scumbag thief. He had family power and a long, strong association with Neil Dellacroce. He was successful as a gangster. Drugs, sure, but who moralizes in LCN? He was a high flyer who didn't fly beneath the radar - he WANTED attention. He was unforgettable: he had fans & wasn't interested in staying in the shadows.
"It was all crap, right up to the moment he died" - an investigator's opinion - and epitaph - of John Holmes (Johnny Wadd)